Pay down mortgage to then cash out refinance?

[Dima R.]

In Long-Distance Real Estate Investing, Greene discusses amortization and the benefits of paying down loans quickly. At the end of Chapter 4, he writes, "...why not reinvest that income into new properties? Pay down your loans faster, refinance them, and then reinvest that chunk of tax-free income into a new multifamily property or several single-family properties?"

Sorry if this is painfully obvious to toehrs - I'm just starting out - but are loans generated by cash out refinancing typically at much lower rates than the initial conventional or commercial loans through which rental properties are typically purchased? And if not, what's the benefit of aggressively paying down a mortgage, only to then cash out refinance? Wouldn't it be the same to pay the mortgage down at a slow rate and then use the excess funds to invest in new property?

Thanks.